# Thread: Hyperplane, any clear explaination?

1. ## Hyperplane, any clear explaination?

Hi math guys,

I am happy to join you in this forum (I also like the fractal symbol) . My math background is not that good , that is why I am looking for clear explanation (examples, figures,...etc) rather than equations and symbols.
I have tried to understand the hyperplane and its relationship to the plane but I can't. I appreciate any help.

Best regards,

2. Originally Posted by ibrex77
Hi math guys,

I am happy to join you in this forum (I also like the fractal symbol) . My math background is not that good , that is why I am looking for clear explanation (examples, figures,...etc) rather than equations and symbols.
I have tried to understand the hyperplane and its relationship to the plane but I can't. I appreciate any help.

Best regards,
In a nutshell:

In $\displaystyle \mathbb{R}^2$, a hyperplane is a line of the form $\displaystyle ax+by=c$ (note that this is the standard form of a line).

In $\displaystyle \mathbb{R}^3$, a hyperplane is our ordinary plane of the form $\displaystyle ax+by+cz=d$ (note that this is the standard form of a plane).

Now, hyperplanes (in general) are planes in $\displaystyle \mathbb{R}^n$. They are of the form $\displaystyle \sum_{i=1}^n a_ix_i=b\implies a_1x_1+a_2x_2+\ldots+a_nx_n=b$.

Unfortunately, there is no real way to visualize these things in 4 or more dimensions!

Does this little bit make sense?

3. ## Thanks

This is just what I am looking for. using line and plane which are somethings I already know to define the hyperplane is really a great idea .

Thank you again .